Metric entropy in linear inverse scattering

Maisto, Maria Antonia; Solimene, Raffaele; Pierri, Rocco

doi:10.7716/aem.v5i2.396

Cited by 19 publications

(6 citation statements)

References 11 publications

(17 reference statements)

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“…The latter, in turns, is of crucial importance while adopting a regularized inverse filtering scheme to achieve the reconstruction. Moreover, since the singular value of A presents an abrupt decay beyond a critical index (the so-called number of degrees of freedom, NDF [19]- [22]), (10) generally returns a good approximation of the psf that a regularized inverse filtering method would yield (unless a very high unfeasible signal to noise ratio is available). Indeed, the number of sampling points is actually linked to the NDF.…”

Section: Sampling Strategymentioning

confidence: 99%

“…To overcome the related huge computational burden, many methods, based on convex optimization, greedy methods and heuristics, have been proposed [17], [18]. However, such methods select the measurement points by running iterative procedures and generally require a a priori information on the problem number of degrees of freedom (NDF) [19]- [22].…”

Section: Introductionmentioning

confidence: 99%

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Sensor Arrangement in Through-the Wall Radar Imaging

Maisto

Masoodi

Pierri

et al. 2022

IEEE Open J. Antennas Propag.

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In this paper, the problem of how to spatially sample the scattered field in microwave through-the wall imaging is addressed. To this end, a two-dimensional scalar configuration for a three-layered back-ground medium is considered under a linearized scattering model. The aim is to collect as low as possible measurements by maintaining the same performance in the reconstructions. Accordingly, the number and the positions of the spatial measurement points are determined so that the point-spread function of the resulting semi-discrete problem approximates well the one of the ideal continuous case (i.e., when data space is not sampled at all). It is shown that the resulting measurement spatial positions must be non-uniformly arranged across the measurement domain and their number is generally much lower than the one returned by some literature sampling criteria. Also, the measurement points can be analytically determined by taking into account the geometrical parameters as well as the wall features. Numerical examples are included to check the theoretical arguments.

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Section: Sampling Strategymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sensor Arrangement in Through-the Wall Radar Imaging

Maisto

Masoodi

Pierri

et al. 2022

IEEE Open J. Antennas Propag.

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“…The number of degrees of freedom of the radiated field (NDF) [18], [19], depending on the size of the source and the measurement aperture, can be much lower than the number of points returned by the λ/2 sampling [20]. This fact has been indeed exploited in [21], where the so-called warping method was introduced and used to derive a new deterministic near-field sampling strategy.…”

Section: Introductionmentioning

confidence: 99%

Non-Uniform Warping Sampling for Data Reduction in Planar Array Diagnostics

et al. 2022

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The problem of detecting defective turned-off elements in antenna arrays from near-field measurements is addressed. In particular, the focus here is to reduce the number of measurements in order to positively affect the acquisition time. Such an issue is achieved by adopting the recently developed warping sampling method. Two commonly antenna diagnostics methods, i.e, the Back Transformation Method (BTM) and the Matrix Method (MM), are considered in view of this new sampling strategy and compared to the usual half-wavelength sampling. In particular, in order to identify the fault locations, outcomes returned by BTM and MM undergo a detection step based on a cell-averaging CFAR (CA)-CFAR technique borrowed from the radar literature. It is shown that the warping sampling method provides performance close to the uniform half-wavelength one with a reduced number of data. Numerical simulations are carried out in order to verify the results with different fault layouts and tapered currents. INDEX TERMS Antenna measurements, Sampling methods, Array diagnostics, Inverse imaging, Nonuniform sampling

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“…In particular, the far-field Green function, i.e., the kernel of the scattering operator, behaves similarly to an entire function of exponential type. This results in an abrupt decay of the singular values beyond a certain critical index, the so-called number of degrees of freedom (NDF) [ 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ] of the scattered field. This singular value behavior, on one hand, is the result of the ill-posedness of the problem [ 31 , 32 ], which limits the achievable performance in the reconstructions.…”

Section: Introductionmentioning

confidence: 99%

Scattered Far-Field Sampling in Multi-Static Multi-Frequency Configuration

Maisto

Masoodi

Leone

et al. 2021

Sensors

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This paper deals with an inverse scattering problem under a linearized scattering model for a multi-static/multi-frequency configuration. The focus is on the determination of a sampling strategy that allows the reduction of the number of measurement points and frequencies and at the same time keeping the same achievable performance in the reconstructions as for full data acquisition. For the sake of simplicity, a 2D scalar geometry is addressed, and the scattered far-field data are collected. The relevant scattering operator exhibits a singular value spectrum that abruptly decays (i.e., a step-like behavior) beyond a certain index, which identifies the so-called number of degrees of freedom (NDF) of the problem. Accordingly, the sampling strategy is derived by looking for a discrete finite set of data points for which the arising semi-discrete scattering operator approximation can reproduce the most significant part of the singular spectrum, i.e., the singular values preceding the abrupt decay. To this end, the observation variables are suitably transformed so that Fourier-based arguments can be used. The arising sampling grid returns several data that is close to the NDF. Unfortunately, the resulting data points (in the angle-frequency domain) leading to a complicated measurement configuration which requires collecting the data at different spatial positions for each different frequency. To simplify the measurement configuration, a suboptimal sampling strategy is then proposed which, by an iterative procedure, enforces the sampling points to belong to a rectangular grid in the angle-frequency domain. As a result of this procedure, the overall data points (i.e., the couples angle-frequency) actually increase but the number of different angles and frequencies reduce and lead to a measurement configuration that is more practical to implement. A few numerical examples are included to check the proposed sampling scheme.

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Metric entropy in linear inverse scattering

Cited by 19 publications

References 11 publications

Sensor Arrangement in Through-the Wall Radar Imaging

Sensor Arrangement in Through-the Wall Radar Imaging

Non-Uniform Warping Sampling for Data Reduction in Planar Array Diagnostics

Scattered Far-Field Sampling in Multi-Static Multi-Frequency Configuration

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